Apparatuses of this kind are used e.g. for fiberizing or screening of waste paper, whereby the drum mantle is usually divided into two parts separated by a partition wall. The part in the inlet end is non-perforated and the one in the outlet end perforated. In the first, non-perforated part of the drum the material to be treated is wetted, treated with chemicals and fiberized and in the other, perforated part it is screened. Drums of this kind are disclosed e.g. in the German published patent application 2651198 and the U.S. patent application Ser. No. 367,179. The partition wall which forms an overflow sill determines the residence time of the material in the fiberizing zone. It is known to provide the drum with a fixed lifting member (a bucket) which lifts the treated material over the partition wall to the next treating zone.